Apologies; I realize this is both not very clearly written, and full of holes when considered as a formal proof. I have a decent excuse in that I had to rush out the door to go to the HPMOR meetup right after writing it. Rereading it now, it still looks like a sketch of a compelling proof, so if neither jimrandomh nor any lurkers see any obvious problems, I'll write it up as a longer paper, with more rigorous math and better explanations.